Translating statements into equations Setting up word problems
1) Define variables clearly. 2) Translate each statement. 3) Put all variables on the left
side of the equal sign and a constant on the right.
Sample statement 1: A farmer plants 3 times as many acres of corn as of wheat.
1) c= the number of acres of corn.
Note: "c=corn" does NOT make sense.
w=the number of acres of wheat
2) c = 3w Why is w multiplied by 3? There is more corn, so c is bigger. w must be
tripled to equal c.
3) c - 3w = 0
The same information could have been given as "A farmer plants one third as much
wheat as corn." Then we would say w = (1/3)c which is (1/3)c-w = 0.
Sample statement 2. A farmer plants corn, wheat and soybeans. He wants half of his total
acres in soybeans.
1) c and w are as above. s = the number of acres of soybeans
2) His total number of acres is c+w+s. s is to be half of this so
s=0.5(c+w+s)
3) -0.5c - 0.5w +0.5s=0
Example 1. Set up only.
A pet store has 108 sq.ft. of space for puppies and kittens. Each puppy needs 9
sq.ft. of space and each kitten needs 4 sq.ft. The store can purchase puppies for $50 each
and kittens for $30 each. They have $670 available for the purchase of puppies and
kittens. How many puppies and kittens should they purchase to use all available space
and money?
1) p=the number of puppies purchased k=the number of kittens purchased
Note: "p=puppies" is unacceptable
2) 9p + 4k = 108
50p+30k=670 which completes the problem.
Example 2. Set up only.
A nut mix is made of peanuts, cashews and pecans. The mixture weighs 7 pounds
and costs $3.50 per pound. Peanuts cost $2.00 per pound, cashews cost $4.10 per pound,
and pecans cost $5.00 per pound. The weight of pecans in the mix is half the weights of
the peanuts and cashews combined. How many pounds of each type of nut does the 7
pound mix contain?
1) x=the number of pounds of peanuts, y=the number of pounds of cashews, z=the
number of pounds of pecans
2) weight: x+y+z=7
cost: 2x + 4.1y+5z=24.50 (that is 7 pounds at 3.5 per pound)
ratio: z=0.5(x+y)
3) x+y+z=7
2x+4.1y+5z=24.5
-0.5x-0.5y+z = 0